Studying the fine properties of solutions to Stochastic (Partial) Differential Equations with
reflection at a boundary this book begins with a discussion of classical one-dimensional
diffusions as the reflecting Brownian motion devoting a chapter to Bessel processes and moves
on to function-valued solutions to SPDEs. Inspired by the classical stochastic calculus for
diffusions which is unfortunately still unavailable in infinite dimensions it uses
integration by parts formulae on convex sets of paths in order to describe the behaviour of the
solutions at the boundary and the contact set between the solution and the obstacle. The text
may serve as an introduction to space-time white noise SPDEs and monotone gradient systems.
Numerous open research problems in both classical and new topics are proposed.
